Yes, as Cost pointed out, the media would have been all over the story from the time she pulled out to the New Hampshire primary and that likely would have spelled doom. But when all is said and done, only Cost's fourth reason is right.
Fourth, and most important of all, she could very well win Iowa! It seems clear to me that the differences in the polling data we have seen is dependent upon the turnout models that the pollsters are using. Under certain assumptions, Clinton leads in the polling. Under other assumptions, she does not. This implies that if those favorable assumptions hold today, Clinton will win the caucus. This would be a huge boost to her candidacy. The shot at winning the first contest is worth the risk of competing.Yes, Clinton could win given certain occurances. But the real problem with Clinton if she had pulled out would have been the loss of perception that she should win the nomination.
Perception in the primary is everything and given the extremely short calendar of primaries, Hillary Clinton cannot afford to lose any perception that she should win the Democratic primary. Even before today, Clinton is battling a growing perception that she is not so inevitable. A strong showing by Obama in Iowa jeopardizes her ability to win in New Hampshire and later.
I am not saying Clinton needs to win in Iowa, but she can't afford to get smoked either. If she loses too badly, and by badly I mean less than about 20 percent of the Iowa vote, she may not recover by New Hampshire. Had she not been in Iowa, she would have been all but guaranteed a loss by a huge margin.
Clinton had to stay in Iowa to maintain the perception that she can win the nomination, even if she can't win in Iowa.